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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Figure 11.41 shows how sandbags placed around a leak outside a river levee can effectively stop the flow of water under the levee. Explain how the small amount of water inside the column formed by the sandbags is able to balance the much larger body of water behind the levee.Figure 11.41 Because the river level is very high, it has started to leak under the levee. Sandbags are placed around the leak, and the water held by them rises until it is the same level as the river, at which point the water there stops rising.

The amount of water inside the sandbag has a pressure equivalent to that of the water in the river.

See the step by step solution

## Step 1: Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

## Step 2: Describing the scenario

The water level behind the levee rose. In order to prevent flooding, sandbags are used and placed at the leaking point. Sandbags are located across the leak, and the water held with the aid of using them rises only to a level that is equal to the water level in the river.

Here, the pressure exerted by water in the sandbags on the river water is reduced.

The river in turn exerts pressure on the water inside the column of sandbags. This pressure prevents a further rise in the water level.

$\mathbit{P}\mathbf{=}\mathbit{h}\mathbit{\rho }\mathbit{g}$

Where h is the height of the air column, ρ is the density of air, and g is the acceleration due to gravity.

## Step 3: Explaining the reason behind the rising level limit of water inside the column formed between the sandbag

Pressure is directly related to height, density, and acceleration due to gravity. In both scenarios, since the density and acceleration due to gravity are the same for the water, in order to balance the pressure, their heights have to be equal. So, when the water level in the bag is equal to the water level in the river, the pressure is balanced. It is enough to prevent further leakage.

Therefore, the level of water inside the column developed by the sandbag rises to the level of river water in order to balance the pressure.